CN112989371A - Multi-image encryption and decryption method based on Walsh transform and computational ghost imaging - Google Patents

Multi-image encryption and decryption method based on Walsh transform and computational ghost imaging Download PDF

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CN112989371A
CN112989371A CN202110230376.1A CN202110230376A CN112989371A CN 112989371 A CN112989371 A CN 112989371A CN 202110230376 A CN202110230376 A CN 202110230376A CN 112989371 A CN112989371 A CN 112989371A
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汪小刚
朱昂昂
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Zhejiang Lover Health Science and Technology Development Co Ltd
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Abstract

The invention discloses a multi-image encryption and decryption method based on Walsh transform and computational ghost imaging, which comprises the following steps: Walsh-Hadamard compression transformation is carried out on a plurality of plaintext images, Arnold scrambling transformation is carried out on a plurality of effective pixels, then the used object plane light intensity is loaded into a ghost imaging calculation light path in sequence, and a target image is encrypted into a ciphertext sequence; secondly, decryption: in the decryption process, the corresponding plaintext image is successfully decrypted by measuring key recovery, compression algorithm reconstruction, inverse Arnold transform and inverse Walsh-Hadamard transform with a correct key set. The image encryption method provided by the invention has the advantages of simple encryption operation, high decryption efficiency and high safety.

Description

Multi-image encryption and decryption method based on Walsh transform and computational ghost imaging
Technical Field
The invention relates to the technical field of information security, in particular to a multi-image encryption and decryption method based on Walsh transform and computational ghost imaging.
Background
In recent years, the development of information technology brings great convenience to people, but at the same time, information security also brings serious challenges to people. Some optical methods for information security, such as optical image encryption, image hiding, and authentication, are receiving increasing attention. Among them, the optical dual-random phase encoding technology based on the 4f system is widely applied. However, the dual random phase encoding technique needs to record the amplitude and phase of information during encryption, and both the encryption efficiency and the decryption efficiency are not high.
Ghost imaging is a new imaging technique based on the correlation between separate but related light fields. Conventional ghost imaging typically uses a large number of random speckle images for illumination and image reconstruction, with the imaging quality typically being proportional to the number of random speckles. Ghost imaging has been used for image encryption due to its physical advantages, using a bucket detector without spatial resolution to record a series of ciphertext sequences. In 2010, clement and Dur-n encrypted the image information into the bucket detector using a computational ghost imaging algorithm and decryption was done using a classical ghost imaging correlation algorithm.
At present, most encryption methods based on ghost imaging adopt a large number of random phases as keys to encrypt images, and adopt an optical means during decryption. Because these methods need to store and transmit a large amount of random phases, the number of measurements and data are very large, and thus the practical application of these methods is still limited.
Disclosure of Invention
The invention aims to provide a multi-image encryption and decryption method based on Walsh transform and computational ghost imaging. The invention can effectively encrypt multiple images and has the advantages of simple encryption operation, high decryption efficiency and high safety.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: a multi-image encryption and decryption method based on Walsh transform and computational ghost imaging is characterized in that: comprises the following steps of encryption:
s1, performing Walsh-Hadamard transform on the multiple images to obtain compressed sparse images, extracting partial pixels in energy sets in all the sparse images to form pixel sets, and recombining the pixel sets according to a zigzag index sequence to obtain a recombined image;
s2, performing sign taking operation on the reconstructed image to obtain a sign matrix containing each pixel, performing constant decomposition on the sign matrix to obtain a group of amplitude plate pairs, and performing Fresnel diffraction on the amplitude plate pairs to generate object plane light intensity;
s3, carrying out absolute value taking operation on the reconstructed image to obtain a matrix containing the absolute value of each pixel, and carrying out Arnold scrambling transformation on the absolute value matrix once to obtain a target image;
s4, taking the target image as an input image of the ghost imaging system, projecting the target image by utilizing the light intensity of the object plane to obtain intensity pairs, calculating the difference value between the intensity pairs to obtain an intensity value, combining all the intensity values to form a ciphertext sequence, and finishing encryption;
and (3) decryption:
rearranging the light intensity of the object plane into corresponding row vector pairs, calculating the difference value between the row vector pairs to obtain row vectors, sequentially arranging the row vectors from top to bottom according to the sequence numbers to form a measurement matrix, executing a compressed sensing reconstruction algorithm with the ciphertext sequence to recover the target image, and finally restoring the image according to the zigzag pixel index sequence by using inverse Arnold transformation to finish decryption.
In the above-mentioned multi-image encryption and decryption method based on walsh transform and computational ghost imaging, the formula obtained for the pair of amplitude plates in step S2 is as follows:
Figure RE-GDA0003064354470000031
in the formula: pW +And PW -Two amplitude plate pairs consisting of 0 and 1 respectively;
Figure RE-GDA0003064354470000032
IWHT[]representing inverse Walsh-Hadamard transforms, (m, n), (x)0,y0) Respectively representing spatial coordinates, delta, before and after the inverse Walsh-Hadamard transformW(m, n) is a two-dimensional impulse function,
Figure RE-GDA0003064354470000033
the above-mentioned multi-image encryption and decryption method based on Walsh transform and computational ghost imaging, generation of the object plane light intensityThe process is as follows: irradiating the amplitude plates P with parallel light of wavelength lambdaWi +,PWi -A distance z in the propagation direction1The diffracted light field at (A) is represented as the primary wavelength of the amplitude plate at λ and the distance at z1The recorded diffraction light intensity is the object plane light intensity:
Figure RE-GDA0003064354470000034
Figure RE-GDA0003064354470000035
wherein FrT [ alpha ]]Representing the Fresnel transformation, (x, y) representing the coordinates of the Fresnel diffraction output plane, | luminance2Indicating the operation of recording the diffracted intensity.
In the multi-image encryption and decryption method based on walsh transform and computational ghost imaging, the process of obtaining the target image by performing Arnold scrambling transform on the absolute value matrix is as follows:
Figure RE-GDA0003064354470000041
where a, b and N are positive integers, a, b and the number of Arnold transformations as decryption keys, N represents the width of the new matrix, mod () is a modulo operation, (x)n,yn) Is the pixel coordinate of the new matrix, (x'n,y′n) Is (x)n,yn) The coordinates of the object after the transformation are obtained,
Figure RE-GDA0003064354470000042
is an invertible matrix.
In the aforementioned multi-image encryption and decryption method based on walsh transform and computational ghost imaging, in step S4, intensity pairs D are measured and recorded using a barrel detectorWi +And DWi -I.e. by
DWi +＝SUM[IWi +(x,y)T(x,y)]
DWi -＝SUM[IWi -(x,y)T(x,y)]；
Wherein SUM () represents a SUM operation on all elements of the matrix; t (x, y) is the target image, and (x, y) represents the coordinates of the Fresnel diffraction output plane;
calculating DWi +、DWi -The difference between them is used to obtain an intensity value DWiNamely:
DWi＝DWi +-DWi -
DWito compute the ith ciphertext of the ghost image, all the ciphertexts are combined to form a ciphertext sequence.
In the aforementioned multi-image encryption and decryption method based on walsh transform and computational ghost imaging, the process of recovering the target image in the decryption step is as follows:
Figure RE-GDA0003064354470000043
where T represents the target image T (x, y),
Figure RE-GDA0003064354470000044
l represents1Norm, argmin (·) represents the minimum value that satisfies the condition.
In the aforementioned multi-image encryption and decryption method based on walsh transform and computational ghost imaging, the decryption step uses the inverse Arnold transform as follows:
Figure RE-GDA0003064354470000051
wherein
Figure RE-GDA0003064354470000052
Is that
Figure RE-GDA0003064354470000053
Corresponding inverse matrices, a, b and N are positive integers, a, b and the number of Arnold transformations as decryption keys, N represents the width of the new matrix, mod () is a modulo operation, (x'n,y′n) Is (x)n,yn) Transformed coordinates, (x)n,yn) Is the pixel coordinates of the new matrix.
Compared with the prior art, the method combines the image Walsh-Hadamard compression transform and the principle of calculating ghost imaging coding, and encrypts and generates an intensity sequence as a ciphertext sequence, so that a large number of keys do not need to be transmitted, and the problem of key template information leakage existing in most image encryption methods is solved; the encryption process and the decryption process respectively adopt the ghost image calculation coding and decoding modes, so that optical holographic recording of phases is not needed, the process is simpler, and simultaneously Arnold transformation is introduced in the operation process and combined with a ciphertext sequence, so that the safety of the system is improved. The invention can effectively encrypt multiple images and has the advantages of simple encryption operation, high decryption efficiency and high safety. In addition, the invention uses the total variation regularization compressed sensing recovery algorithm, so that the iterative convergence speed is higher, and the quality of the reconstructed image is higher.
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Fig. 1 is a flow chart of an encryption process.
Fig. 2 is a flowchart of the decryption process.
FIGS. 3(a) - (d) are a plurality of plaintext images; (e) an encrypted amplitude plate key; (f) one of the symbol keys obtained by constant decomposition; (g) a pixel mosaic; (h) and (4) obtaining a graph to be encrypted after Arnold transformation.
FIG. 4 computes a ghost image decoding map and a final decryption map. (a) Compressing a ghost imaging decoding image; (b) inverse Arnold transform of the resulting profile; (c) - (f) correct indexing of the keys to obtain the final decrypted graph.
FIG. 5 is a graph of an analysis. (a) Adding white Gaussian noise with different degrees into the ciphertext image, and obtaining a relation graph between Correlation Coefficients (CC) between the four plaintext images and the decrypted image and the noise intensity; (b) and a relation graph between the correlation coefficient between the original image Lena and the image obtained by final decryption and the corresponding ciphertext quantity.
FIG. 6 is a "Lena" decrypted image obtained when the decryption key is erroneous; (a) a decrypted image obtained when the wrong measurement matrix is decrypted; (b) a decrypted image obtained when the wrong Arnold transformation key is decrypted; (c) and a decrypted image obtained when the wrong symbol key is decrypted.
Detailed Description
The present invention will be further described with reference to the following examples and drawings, but the present invention is not limited thereto.
Example (b): a multi-image encryption and decryption method based on walsh transforms and computational ghost imaging, comprising the encryption steps as shown in fig. 1:
s1, for multiple images fi(i 1,2,3 … N) (Target images in fig. 1) to perform walsh-hadamard transform to obtain compressed sparse image gi(Compress imges in FIG. 1), i.e. gi(x0,y0)＝WHT[fi(m,n)]Wherein WHT [ alpha ], [ alpha ]]Representing Walsh-Hadamard transform, all sparse images g are extractediForming a pixel set Pix (x, y) by the pixels in the middle energy set, and recombining the pixel set according to the index sequence of the zigzag to obtain a recombined image B (x, y) (the reconstructed image in FIG. 1); i.e. B (x, y) ═ RA { Pix (x, y) }, where RA { } represents the glyph extraction operation, i.e. the pixels in the sequence of extraction matrices are extracted according to a glyph scan;
s2, obtaining a symbol matrix sign { B (x, y) } containing each pixel of the recombined image B (x, y) after carrying out symbol taking operation on the recombined image B (x, y), wherein sign { } is a symbol taking operator, the symbol matrix consists of +/-1 only, and then carrying out constant decomposition on the symbol matrix sign { B (x, y) } to obtain a group of amplitude-vibrating plate pairs, wherein the obtained formula of the amplitude-vibrating plate pairs is as follows:
Figure RE-GDA0003064354470000071
in the formula: pW +And PW -Two amplitude plate pairs consisting of 0 and 1 respectively;
Figure RE-GDA0003064354470000072
IWHT[]representing inverse Walsh-Hadamard transforms, (m, n), (x)0,y0) Respectively representing spatial coordinates, delta, before and after the inverse Walsh-Hadamard transformW(m, n) is a two-dimensional impulse function,
Figure RE-GDA0003064354470000073
then, the amplitude plate pair is subjected to Fresnel diffraction to generate object plane light intensity:
irradiating the amplitude plates P with parallel light of wavelength lambdaWi +,PWi -A distance z in the propagation direction1The diffracted light field at (A) is represented as the primary wavelength of the amplitude plate at λ and the distance at z1The recorded diffraction light intensity is the object plane light intensity:
Figure RE-GDA0003064354470000083
Figure RE-GDA0003064354470000084
wherein FrT [ alpha ]]Representing the Fresnel transformation, (x, y) representing the coordinates of the Fresnel diffraction output plane, | luminance2Indicating the operation of recording the diffracted intensity.
S3, performing an absolute value operation on the reconstructed image B (x, y) to obtain a matrix abs { B (x, y) } containing the absolute value of each pixel, and performing an Arnold scrambling transform on the absolute value matrix abs { B (x, y) } to obtain a target image T (x, y) (AST image in fig. 1), where the process is shown as follows:
Figure RE-GDA0003064354470000081
where a, b and N are positive integers, a, b and the number of Arnold transformations as decryption keys, N represents the width of the new matrix, mod () is a modulo operation, (x)n,yn) Is a new momentPixel coordinates of matrix, (x'n,y′n) Is (x)n,yn) The coordinates of the object after the transformation are obtained,
Figure RE-GDA0003064354470000082
is an invertible matrix.
S4, using the object plane light intensity I and using the target image T (x, y) as the input image of the ghost imaging systemWi +(x, y) and IWi -(x, y) projecting the target image separately, measuring and recording the intensity pair D with a barrel detectorWi +And DWi -I.e. by
DWi +＝SUM[IWi +(x,y)T(x,y)]
DWi -＝SUM[IWi -(x,y)T(x,y)]；
Wherein SUM () represents a SUM operation on all elements of the matrix; t (x, y) is the target image, and (x, y) represents the coordinates of the Fresnel diffraction output plane;
calculating DWi +、DWi -The difference between them is used to obtain an intensity value DWiNamely: dWi＝DWi +-DWi -
DWiIn order to calculate the ith Ciphertext of the ghost image, all the ciphertexts are combined to form a Ciphertext sequence (Ciphertext in figure 1) to finish encryption;
and (3) decryption:
as shown in FIG. 2, the object plane is illuminated by a light intensity IWi +(x, y) and IWi -(x, y) are rearranged into corresponding pairs of row vectors IWi +(x) And IWi -(x) Calculating the difference between the row vector pair to obtain a row vector IWi(x) I.e. that
IWi(x)＝IWi +(x)-IWi -(x)
The row vectors are sequentially arranged from top to bottom according to the sequence number i to form a measurement matrix phi, and a compressed sensing reconstruction algorithm is executed with the ciphertext sequence to recover a target image, wherein the process is as follows:
Figure RE-GDA0003064354470000091
where T represents the target image T (x, y),
Figure RE-GDA0003064354470000092
l represents1Norm, argmin (·) represents the minimum value that satisfies the condition.
And finally, restoring the image by using inverse Arnold transformation according to the return-font pixel index sequence, wherein the process is as follows:
Figure RE-GDA0003064354470000093
wherein
Figure RE-GDA0003064354470000094
Is that
Figure RE-GDA0003064354470000095
Corresponding inverse matrices, a, b and N are positive integers, a, b and the number of Arnold transformations as decryption keys, N represents the width of the new matrix, mod () is a modulo operation, (x'n,y′n) Is (x)n,yn) Transformed coordinates, (x)n,yn) Is the pixel coordinates of the new matrix.
And finally, the decryption is completed.
The invention is further explained below with reference to specific examples.
First, as shown in fig. 3, four gray-scale maps "monke y" (fig. 3 (a)), "barbarbara" (fig. 3 (b)), "Boat" (fig. 3 (c)), "Lena" (fig. 3 (d)) having a size of 128 × 128 are selected as plaintext images, and an amplitude slab for encryption, which is a matrix composed of only 0,1 and having a size of 128 × 128, is shown in fig. 3(e) and 3 (f). The pixel reconstructed image after the walsh-hadamard compression transform and the image to be encrypted obtained after the Arnold transform are respectively shown in fig. 3(g) and fig. 3 (h).
And obtaining a target image T (x, y) through an encryption process shown in fig. 1, and finally converting the target image T (x, y) into a ciphertext sequence by using a computational ghost imaging technology.
The decryption process is as shown in fig. 2, a reconstructed image is obtained according to the compressed ghost imaging technology, and then a plurality of correct decryption images can be obtained by utilizing inverse Arnold transformation and a correct index sequence.
Fig. 4 shows the calculation of the ghost image reconstruction map and the final decrypted image, wherein fig. 4(a) is the compressed ghost image reconstruction map, fig. 4(b) is the image decrypted by the inverse Arnold transform, and fig. 4(c) -4(f) are the four decrypted images obtained by the correct index key, respectively, and the decrypted images can be effectively identified visually.
The encryption/decryption effect and security of the present invention will be described below by taking decryption of "Lena" image as an example.
Fig. 5(a) shows the variation relationship between the correlation coefficient between the decrypted image and the plaintext image and the noise intensity added by the ciphertext, and it can be seen that the minimum value of the correlation coefficient is greater than 0.4, which indicates that the invention has good anti-noise capability. Fig. 5(b) shows a variation relationship between the correlation coefficient between the original image "Lena" and the corresponding decrypted image and the corresponding ciphertext amount, and when the ciphertext amount is present, the corresponding CC value exceeds 0.5, which indicates that the plaintext image can be effectively recovered by the present invention when the ciphertext amount is relatively small.
The security of the invention is examined below. A pass security test is first performed to verify the security of the measurement matrix, scrambling key and symbol key against errors. The invention uses a controlled variable method, namely only one variable is changed, and the other variables are kept unchanged. When the ghost imaging encryption result is decrypted using the wrong measurement matrix, the resulting decryption result is shown in fig. 6 (a); when decryption is performed using the wrong Arnold transformation key, i.e., the wrong number of Arnold transformations, the obtained decryption result is shown in FIG. 6 (b); when the wrong symbol key is used, the resulting decryption result is shown in fig. 6 (c). The above analysis and experiment results show that the measurement matrix, the scrambling key and the symbol key are three essential elements for realizing image decryption, and when one of the three essential elements has an error, a correct decryption result cannot be obtained.
In conclusion, the invention combines the image Walsh-Hadamard compression transform and the principle of calculating ghost imaging coding, and encrypts to generate an intensity sequence as a ciphertext sequence, so that a large number of keys do not need to be transmitted, and the problem of key template information leakage existing in most image encryption methods is solved; the encryption process and the decryption process respectively adopt the ghost image calculation coding and decoding modes, so that optical holographic recording of phases is not needed, the process is simpler, and simultaneously Arnold transformation is introduced in the operation process and combined with a ciphertext sequence, so that the safety of the system is improved.

Claims (7)

1. A multi-image encryption and decryption method based on Walsh transform and computational ghost imaging is characterized in that: comprises the following steps of encryption:
s1, performing Walsh-Hadamard transform on the multiple images to obtain compressed sparse images, extracting partial pixels in energy sets in all the sparse images to form pixel sets, and recombining the pixel sets according to a zigzag index sequence to obtain a recombined image;
s2, performing sign taking operation on the reconstructed image to obtain a sign matrix containing each pixel, performing constant decomposition on the sign matrix to obtain a group of amplitude plate pairs, and performing Fresnel diffraction on the amplitude plate pairs to generate object plane light intensity;
s3, carrying out absolute value taking operation on the reconstructed image to obtain a matrix containing the absolute value of each pixel, and carrying out Arnold scrambling transformation on the absolute value matrix once to obtain a target image;
s4, taking the target image as an input image of the ghost imaging system, projecting the target image by utilizing the light intensity of the object plane to obtain intensity pairs, calculating the difference value between the intensity pairs to obtain an intensity value, combining all the intensity values to form a ciphertext sequence, and finishing encryption;
and (3) decryption:
rearranging the light intensity of the object plane into corresponding row vector pairs, calculating the difference value between the row vector pairs to obtain row vectors, sequentially arranging the row vectors from top to bottom according to the sequence numbers to form a measurement matrix, executing a compressed sensing reconstruction algorithm with the ciphertext sequence to recover the target image, and finally restoring the image according to the zigzag pixel index sequence by using inverse Arnold transformation to finish decryption.
2. The walsh transform and computational ghost imaging based multiple image encryption and decryption method of claim 1, wherein: the formula obtained for the pair of amplitude plates in step S2 is as follows:
Figure FDA0002957608870000021
in the formula: pW +And PW -Two amplitude plate pairs consisting of 0 and 1 respectively;
Figure FDA0002957608870000022
IWHT[]representing inverse Walsh-Hadamard transforms, (m, n), (x)0,y0) Respectively representing spatial coordinates, delta, before and after the inverse Walsh-Hadamard transformW(m, n) is a two-dimensional impulse function,
Figure FDA0002957608870000023
3. the walsh transform and computational ghost imaging based multiple image encryption and decryption method of claim 2, wherein: the generation process of the object plane light intensity is as follows: irradiating the amplitude plates P with parallel light of wavelength lambdaWi +,PWi -A distance z in the propagation direction1The diffracted light field at (A) is represented as the primary wavelength of the amplitude plate at λ and the distance at z1The recorded diffraction light intensity is the object plane light intensity:
Figure FDA0002957608870000024
Figure FDA0002957608870000025
wherein FrT [ alpha ]]Representing the Fresnel transformation, (x, y) representing the coordinates of the Fresnel diffraction output plane, | luminance2Indicating the operation of recording the diffracted intensity.
4. The walsh transform and computational ghost imaging based multiple image encryption and decryption method of claim 1, wherein: the process of obtaining the target image by performing Arnold scrambling transformation on the absolute value matrix is shown as the following formula:
Figure FDA0002957608870000031
where a, b and N are positive integers, a, b and the number of Arnold transformations as decryption keys, N represents the width of the new matrix, mod () is a modulo operation, (x)n,yn) Is the pixel coordinate of the new matrix, (x'n,y′n) Is (x)n,yn) The coordinates of the object after the transformation are obtained,
Figure FDA0002957608870000032
is an invertible matrix.
5. The walsh transform and computational ghost imaging based multiple image encryption and decryption method of claim 1, wherein: in step S4, intensity pair D is measured and recorded using a barrel probeWi +And DWi -I.e. by
DWi +＝SUM[IWi +(x,y)T(x,y)]
DWi -＝SUM[IWi -(x,y)T(x,y)]；
Wherein SUM () represents a SUM operation on all elements of the matrix; t (x, y) is the target image, and (x, y) represents the coordinates of the Fresnel diffraction output plane;
calculating DWi +、DWi -The difference between them is used to obtain an intensity value DWiNamely:
DWi＝DWi +-DWi -
DWito compute the ith ciphertext of the ghost image, all the ciphertexts are combined to form a ciphertext sequence.
6. The walsh transform and computational ghost imaging based multiple image encryption and decryption method of claim 1, wherein: the process of recovering the target image in the decryption step is as follows:
Figure FDA0002957608870000033
where T represents the target image T (x, y),
Figure FDA0002957608870000034
l represents1Norm, argmin (·) represents the minimum value that satisfies the condition.
7. The walsh transform and computational ghost imaging based multiple image encryption and decryption method of claim 1, wherein: the decryption step uses the inverse Arnold transform as follows:
Figure FDA0002957608870000041
wherein
Figure FDA0002957608870000042
Is that
Figure FDA0002957608870000043
Corresponding inverse matrix, a, b and N are positive integers, a, b and Arnold transform times as decryptionKey, N represents the width of the new matrix, mod () is a modulo operation, (x'n,y′n) Is (x)n,yn) Transformed coordinates, (x)n,yn) Is the pixel coordinates of the new matrix.
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